Reducing the gain in the circuit will reduce risk of instability/oscillation BTW.
Filtering out any RF on inputs is always a good idea for sensitive DC circuits like this - 1nF ceramic across all the load-cell input leadsshould kill any RF pickup without affecting the frequencies of interest. Ferrite toroid on the whole lead close to the breadboard isalso another possibility.Definitely keep all the wiring on the breadboard short and neat and supply decoupling capacitors are _obligatory_ for a high-gain amplifier, otherwise it is very likely to oscillate via supply-rail feedback. A ground-plane would be nice, though obvious difficult on a breadboard. One can add a grid of ground wires across the whole breadboard toimprove matters.Reducing the gain in the circuit will reduce risk of instability/oscillation BTW.